Sustainable Urban Stormwater Management Research Articles

The Application of Rain Gardens in Urban Environments: A Bibliometric Review

The increasing challenges of urbanization and climate change have driven the need for innovative stormwater management solutions. Rain gardens, as a nature-based solution (NBS), have emerged as a critical component in urban water management, particularly in enhancing hydrological regulation, water quality, and ecosystem services. This bibliometric review examines the application of rain gardens in urban environments, focusing on their roles in stormwater management, pollutant removal, and ecological enhancement. Data from 728 academic papers published between 2000 and 2023 were analyzed using the Web of Science (WoS) Core Collection, employing bibliometric tools such as the “Bibliometrix” R package and CiteSpace. The analysis highlights the increasing global interest in rain gardens, particularly since 2015, with China and the United States leading research efforts. Key findings reveal that rain gardens significantly reduce runoff, improve water quality, and contribute to urban biodiversity. In addition, their integration into public spaces offers landscape esthetics and social benefits, enhancing the quality of life in urban areas. However, challenges remain in optimizing their design for diverse climates and long-term performance. The study underscores the need for further research on plant–soil interactions, pollutant removal mechanisms, and the broader ecological and social contributions of rain gardens. This review provides insights into the evolution of rain garden research and identifies future directions for advancing sustainable urban stormwater management.

Multi-objective optimization of distributed green infrastructure for effective stormwater management in space-constrained highly urbanized areas

Green infrastructure (GI) is essential for stormwater management, but its implementation in highly urbanized areas is challenging due to the limited space available for GI retrofitting. There is a lack of comprehensive evaluations that assess the spatial adaptability, functionality, and cost-benefit of various GI measures, and optimize their placement to achieve the maximum reduction rate of total runoff (RTR) and reduction rate of pollution load (RPL) while minimizing life cycle cost (LCC) in space-constrained highly urbanized areas (SCHUA). To address this issue, a novel concept of infiltration, retention, and storage integrated GI (IRS-GI) for SCHUA was proposed, and a framework coupling the Storm Water Management Model (SWMM) with multi-objective optimization algorithms was developed to determine the optimal IRS-GI layout, focusing on the objectives of RTR, RPL, and LCC. The impacts of different GI type, size, and location, rainfall return periods, and algorithms (NSGA-II and NSGA-III) were then examined. The results showed that IRS-GI could achieve satisfactory RTR and RPL results while single-type GI may struggle to meet requirements. Optimization outcomes were significantly influenced by rainfall return periods, with cost-benefit decreasing as return periods increasing. Besides, the optimization results of NSGA-II and NSGA-III showed differences, and the comprehensive Pareto frontier obtained by reapplying non-dominated sorting could achieve more comprehensive results for determining the optimal IRS-GI configuration. Under the urban drainage design standard, the optimal IRS-GI layout, covering 32.97 % of the green spaces, 38.57 % of the rooftop, and 60.98 % of the ordinary roads and squares, respectively, could achieve a RTR of 50.09 %, RPL of 57.00 %, and LCC of 0.79 × 108 CNY/yr. Additionally, the optimal configuration suggested that a higher proportion of GI downstream of drainage system may contribute to better cost-benefit, emphasizing the need for location-specific GI solutions. This research offers valuable insights for optimizing GI in SCHUA, advancing sustainable urban stormwater management.

Community perception towards sustainable urban stormwater management practices: a case study in Thu Duc City, Vietnam

Abstract Sustainable urban Stormwater Management (SSM) is currently widely implemented globally to support urban flood management efforts. It is commonly known by terms such as Green Infrastructure (GI), Best Management Practice (BMP), Sustainable Urban Drainage System (SUDS) or Low Impact Development (LID). However, in Vietnam, these approaches are still relatively new and have not been widely adopted due to various barriers, including community perception. Therefore, this study conducted a preliminary social survey in the Thu Duc City area to gain a deeper understanding of perspectives, knowledge, and support for SSM practices. The results showed that among the surveyed residents, 78% favored a centralized stormwater management manner (e.g., retention/detention ponds,…), 51% preferred a decentralized manner (e.g., rain gardens, infiltration trenches,…) and 45% considered household-level practices (e.g., green roofs, rain barrels,…). Additionally, when asked about financial contributions towards implementing these practices, approximately 70% did not support the idea, and 50% believed it was the government’s responsibility. The research findings highlight the diversity in urban residents’ perceptions and opinions regarding stormwater management. This study provides essential foundational information for the development of policies and strategies to effectively promote SSM practices, aiming to mitigate urban flooding and contribute to environmental protection.

Establishing rainfall intensity-duration-frequency curves for Baghdad, Iraq using satellite data

Abstract Rainfall intensity-duration-frequency (IDF) curves were generated for Baghdad by utilising three satellite precipitation datasets: Global Satellite Mapping of Precipitation Near Real-Time (GSMaP NRT), gauge-corrected (GSMaP GC) and Global Precipitation Measurement Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG). Maximum annual rainfall data was fitted using several probability distribution methods. The calculated coefficients from the best-fit distribution were used as fitting parameters to generate IDF curves for return periods of 2, 5, 10, 25, 50 and 100 years using the Sherman equation. To address discrepancies between the satellite-derived IDF curves and observed data, bias correction was performed based on the differences. The analysis revealed that the Generalized Extreme Value Distribution model accurately described the hourly rainfall distribution. GSMaP GC exhibited the highest correlation with the observed data, making it the preferred option for generating IDF curves. The study highlighted the importance of gauge correction for satellite rainfall data to minimise the underestimation or overestimation of rainfall. GSMaP GC demonstrated reasonable accuracy in estimating rainfall in Iraq’s mainly arid climate area. By assisting in the creation of efficient methods for dealing with rainstorm events, the created IDF curves are a major step towards advancing sustainable urban stormwater management in the country.

A critical review on optimization and implementation of green-grey infrastructures for sustainable urban stormwater management

ABSTRACT Green-grey infrastructures' implementation has progressed significantly in cities around the globe for sustainable stormwater management. This review study conducted on green-grey infrastructures' optimization represented recent research trends, existing research status, possible study gaps, and future research directions and recommendations needed for further improvements. The findings show that the research on green-grey infrastructures has got significant attention recently (after 2012) because of accessibility to computational resources and the development of hydrological-hydraulic models and optimization algorithms. Furthermore, research on green-grey infrastructures is mostly conducted in ten countries including China, USA and Iran ranked in the first three places, respectively, delivering their advantages to other countries with the essential awareness and knowledge. Most previous studies considered particular quantitative and qualitative optimization objectives and these studies were conducted at smaller retrofitting scales, therefore, future studies need to expand their scope towards socio-ecological objectives with consideration of larger study areas or multi-stage planning, designing, and implementation. Moreover, future research is recommended to consider stakeholders’ participation in preliminary planning and designing stages for the successful implementation of sustainable stormwater management approaches. Lastly, the surrogate-based optimization approaches instead of traditional optimization methods can overcome the burden of computational time and resources in future.

Risk-driven composition decoupling analysis for urban flooding prediction in high-density urban areas using Bayesian-Optimized LightGBM

With catastrophic climate change and accelerated urbanization, urban flooding has emerged as the most influential hazard over last few decades. Therefore, a systematic study on the assessment of urban flooding vulnerability and evaluation of multidimensional relationship between flooding indicators and inundation depth is imperatively needed. Machine learning methods have been proven to be extremely effective in predicting urban flooding susceptivity based on a multivariate data-driven approach. In the present study, a cascade modeling chain was explored consisting of integrated Light Gradient Boosting Machine (LightGBM) and decoupling analysis of risk-driven composition, based on a multi-factor database consisting of hydro-meteorological, underlying-surfaces, and building configurations indicators. LightGBM was verified to be reliable and robust for urban flooding vulnerability assessment. Taking Shenzhen as a case study, the results indicated that rainfall volume (TOTAL_R), rainfall duration (LTIME), percentage of impervious surface (PIS), building congestion degree (BCD) and density of buildings (DB) were mainly responsible for the increase in flooding risk, while percentage of water coverage (PW) was highly efficient in flooding mitigation. Areas with high flooding risks are concentrated in older metropolitan areas when the rainfall volume surpassed 125 mm or the rainfall duration was longer than 55h. The urban flooding vulnerability was significantly increased when the PIS, BCD, and DB were greater than 14%, 0.58, and 16 n/ha, respectively. It was recommended that adaptation strategies should be implemented in high-density areas to increase urban resilience to extreme rainfall events. The findings of this study can serve as a scientific basis and technical support for sustainable urban stormwater management.

ALTERNATIF PENGENDALIAN LIMPASAN PERMUKAAN DI PERKOTAAN DENGAN MENGGUNAKAN METODE ANALYTICAL HIERARCHY PROCESS (AHP)

Control of surface runoff is a major challenge in sustainable urban stormwater management. High rainfall can cause various problems such as floods and landslides. Related to the problem of surface runoff includes a number of problems that require attention and good solutions to maintain environmental sustainability and prevent negative impacts from surface runoff. Surface runoff control activities generally tend to be social, technically costly, and relatively long. Collaboration with experts, government, and local stakeholders can also reinforce the concept of successful surface runoff control. The application of the AHP (Analytical Hierarchy Process) method is needed as a systematic approach to evaluate and select effective alternative surface runoff control systems, in this study four alternatives were taken based on three criteria. These alternatives involve solutions such as the application of biopores of infiltration wells, rainwater harvesting, retention ponds and green open spaces then these alternatives are evaluated based on relevant criteria, in this study the relevant criteria are taken namely technically, environmentally and cost. The results of this analysis using the AHP method provide relative priority values for each alternative, allowing for the selection of optimal solutions to surface runoff problems. Based on this assessment, it shows that alternative green open space is an optimal solution for surface runoff control systems in urban areas.

A new analytical stormwater model for bioretention systems considering both infiltration and saturation excess runoff generation processes

Bioretention systems are increasingly used as a typical stormwater management measure due to their flexibility of scale and general aesthetic appeal. The main purpose of bioretention systems is to control runoff and their runoff reduction efficiency is affected by parameters such as contributing catchment area, fillings and sizes. Conventional analytical probabilistic studies on bioretention systems only considered saturation excess runoff for simplicity and may cause inaccuracy of estimating runoff. In this study, an analytical stochastic model (ASM) for bioretention systems considering both infiltration-excess and saturation-excess runoff generation processes was derived. The proposed ASM model was validated in a large number of case studies in Guangzhou, Jinan, and Lanzhou, China. Various climate, soil, dimension and land use conditions were investigated and compared. Close agreement was observed between the results obtained from the ASM model and continuous simulation results. The ASM model can be used to conveniently evaluate the runoff reduction efficiency of bioretention systems under different configurations of design parameters. It thus provides a computationally efficient analytical tool for the rapid design, analysis and evaluation of the nature-based solution to sustainable urban stormwater management.

Editorial: Sustainable urban stormwater management under a changing climate

Editorial: Sustainable urban stormwater management under a changing climate

The improved analytical stochastic model of infiltration trenches for stormwater quantity control

As one of the infiltration-based low-impact development (LID) measures, infiltration trenches are widely used to reduce runoff and improve water quality. The conventional analytical stochastic approach developed for use in the hydrologic design of infiltration trenches often overestimates the trench's runoff reduction performance when the infiltration rate at the bottom of the trench exceeds some high level or when the size of the trench is smaller than some threshold level. Furthermore, the appropriateness of using kernel density estimation (KDE) for rainfall event separation and frequency analysis has not been examined yet in the actual hydrologic design of LIDs. To overcome these deficiencies, an improved analytical stochastic model (ASM) was developed in this study incorporating the KDE-based rainfall event characterization and a modified formula for estimating the effective storage capacity of trenches. The calibration, verification and application of the improved ASM were systematically presented and their results were discussed. The accuracy of the improved ASM were verified by comparing the analytical results against the corresponding continuous simulation results. A large number of design cases in nine provincial capital cities of China were analyzed using the improved ASM and considering the effects of soil types, trench's storage reservoir depth, area ratio, and climate conditions. The improved ASM of infiltration trenches is useful for quickly and accurately assessing their water quantity control performances. The results indicated that the accuracy of improved ASM improved by up to 71 % in terms of R-square among the 9 study areas compared to conventional ASM. The improved ASM can be used to directly and quickly calculate the useful hydrologic performance indices for a given trench size, soil condition, area ratio and local climate condition, it can thus provide scientific guidance for the Sponge City construction in China and sustainable urban stormwater management.

Utilizing Satellite Data to Establish Rainfall Intensity-Duration-Frequency Curves for Major Cities in Iraq

This study generates intensity-duration-frequency curves for three important cities in Iraq using Global Precipitation Measurement Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG), Global Satellite Mapping of Precipitation near real-time (GSMaP NRT), and gauge corrected (GSMaP GC) satellite precipitation datasets. Many probability distribution functions were used to fit the maximum yearly rainfall data. The Sherman equation was used to create intensity-duration-frequency (IDF) curves for rainfall intensities with 2-, 5-, 10-, 25-, 50-, and 100-year return periods, with the estimated coefficients of the best-fit distribution serving as the fitting parameters. The discrepancy between the IDF curves produced from the satellites and the observed data was used to bias correct the satellite IDF curves. The Generalized Extreme Value Distribution model best describes the hourly rainfall distribution of satellite data. GSMaP GC was the best option for creating IDF curves with higher correlations with observed data at Baghdad, Basra, and Mosul. The study indicates the necessity of gauge correction of satellite rainfall data to reduce under- and over-estimating observed rainfall. GSMaP GC can reasonably estimate rainfall in a predominantly arid climate region like Iraq. The generated IDF curves may be an important step toward achieving sustainable urban stormwater management in the country.

Implementing effective hydrological rules for sustainable urban stormwater management

Actuellement, en France, de nombreuses collectivités mettent en place un cadre réglementaire et incitatif visant en particulier à favoriser le développement des solutions dites alternatives de gestion des eaux pluviales urbaines. En s’appuyant sur une approche analytique fondée sur la méthode des pluies, ce document s’intéresse aux conséquences négatives que certaines règles hydrologiques peuvent parfois introduire. Ces conséquences négatives sont dues à la diversité des situations hydrologiques que les dispositifs doivent affronter, à la variété des objectifs poursuivis, à la variété en nature et en taille des opérations d’aménagement et, enfin, au grand nombre de solutions techniques possibles. Il montre que si les règles choisies sont trop rigides ou mal conçues elles peuvent avoir des effets pervers, voire même se révéler contre-productives. Au-delà de ce simple diagnostic, il propose des pistes pour améliorer leur rédaction. Il préconise en particulier la mise en oeuvre d’un ensemble de règles complémentaires, construites de façon à privilégier les objectifs locaux perçus comme essentiels, et adaptées aux différents niveaux de sollicitation pluviométrique. Enfin, il fournit quelques éléments pratiques pour les rédiger de façon appropriée.

Vegetated Roofs as a Means of Sustainable Urban Development: A Scoping Review

Urbanisation affects the water cycle and heat balance in a negative way. Vegetated roofs have the potential to minimise the effects of urbanisation. A scoping review is presented here to examine how vegetated roofs are being evolved as an effective tool of sustainable urban stormwater management and overall urban development. It has been found that research on vegetated roofs has been increasing significantly and it can contribute towards achieving multiple sustainable development goals (SDGs). It has also been found that the uptake of vegetated roofs has been slow. A lack of regulatory acceptance caused by an absence of experimental data and a subsequent knowledge gap establishing the effectiveness of vegetated roofs are major reasons behind this slow uptake. Future research on vegetated roofs and their subsequent evolutions should put a focus on gathering experimental data towards establishing a performance benchmark for detention, retention and water quality in urban settings. Such data can be utilised towards developing a stand-alone guideline and software for green roof design.

Transitioning to Sponge City: A Key to Water Resource Management during Floods in Assam

Flooding in the recent times is one of the society’s most significant threats from climate change and dramatic weather events. As such, integrating sponge city construction and green infrastructure have become the new paradigm for a sustainable urban storm water management policy. Sponge city initiative can be implemented in Assam too. After more than seven decades of yearly perennial floods, we know by now that the mighty Brahmaputra cannot be tamed. Nor Assam can fight climate change alone. Sponge city strategy would help Assam to work in unison with nature and sustainably manage rainwater and floodwater which could be a huge advantage not only to the environment but also to the local population as well. This paper aims to suggest certain green infrastructures and sponge city strategies which have been implemented by China and western nations in managing floods. Adopting such strategies may not be able to remove all issues completely but it might definitely work out to reduce the disastrous effect of floods. It will also help to manage water resources efficiently in the State.

Barriers to sustainable urban stormwater management in developing countries: The case of Brazil

Urban stormwater management is one of the key challenges concerning sustainability in urban areas. Sustainable urban stormwater management (SUSM) has been increasingly adopted around the world and proved its effectiveness in enhancing sustainability and quality of life in cities. Nevertheless, these strategies are yet to be widely adopted in developing countries. This paper presents barriers to the widespread adoption of SUSM in Brazil, as a developing country case study with severe urban stormwater management problems. To achieve this objective, a thorough review of literature on the barriers has been conducted. An online survey has been designed and disseminated to different Brazilian participant stakeholder groups (i.e. public professionals, private professionals, teachers, and population) to identify the SUSM-related barriers in Brazil. The reviews recognized 31 potential barriers in literature which were categorized into six barrier types. Five of the evaluated barriers have been recognized by at least 80% of the respondents as the most important, namely: “Lack of design and maintenance standards”, “Lack of long-term planning”, “Lack of dissemination and knowledge”, “Lack of incentives”, and “Reluctance to change”. The barriers identified by this research are coherent with the SUSM adoption context in Brazil. These barriers are mainly related to knowledge about SUSM and similar to those diagnosed in previous studies in literature. Overcoming the common barriers is the prelude to effective SUSM solutions to increase urban stormwater sustainability in Brazil and in other developing countries. This paper also presents some initiatives adopted around the world to overcome these barriers, which could be used as reference to an effective public policy proposition.

The Impacts of Climate Change and Porous Pavements on Combined Sewer Overflows: A Case Study of the City of Buffalo, New York, USA

Combined sewer overflows (CSOs) release pollutants collected in urban runoff into local waterways, impacting both aquatic life and human health. The impact of climate change on precipitation may result in an increase in the frequency and magnitude of heavy precipitation events, with a corresponding increase in CSO discharges. The installation of Green Infrastructure (GI) such as Porous Pavements (PP) is a resilient approach to mitigate CSO events. However, an understanding of the impact of climate change on CSO events and the effectiveness of GI practices is crucial for designing sustainable urban stormwater management systems. Using the Storm Water Management Model (SWMM), the performance of PP as a CSO abatement strategy was studied for the city of Buffalo, New York, USA. This paper used the Intensity-Duration-Frequency (IDF) curves for current (1970–1999) and future (2070–2099) design rainfall scenarios, with four rainfall durations (1, 6, 12, and 24 hours) and four return periods (2, 10, 50, and 100 years). The simulation results show that (1) current 100-year events generate CSO volumes similar to predicted 50-year events; (2) CSO volumes could increase by 11–73% in 2070–2099 compared to 1970–1999 when no GI intervention is performed; and (3) the installation of PP can reduce 2–31% of future CSO volume. This case study demonstrates the regional CSO challenges posed by climate change and supports the use of GI as a mitigation strategy.

A Study on Implementation of Low Impact Development as an Urban Stormwater Management Technique in Srinagar City: Current Trends, Issues and Challenges

Abstract: The Severity as well as the frequency of short-duration, but damaging, urban area floods have increased in recent years across the world. Alteration to the urban micro-climate due to global climate change impacts may also exacerbate the situation in the near future. The events of floods have increased in Srinagar city as well over the past decades. Sustainable urban stormwater management using low impact development (LID) techniques, along with conventional urban stormwater management systems, can be implemented to mitigate climate-change-induced flood impacts in Srinagar. In this study, the supposed effectiveness of LIDs in the mitigation of urban flood in Srinagar city is analysed keeping in view their limitations at the same time. A critical research on the success of these techniques in urban flood mitigation planning in Srinagar city is also recommended. On summarising different LID approaches in the world, the results revealed that LIDs can be an efficient method for mitigating urban flood impacts. Most of the LID devices developed so far, however, are found to be effective only for small flood peaks. The major challenges include identification of the best LID practices for the region of interest, efficiency improvements in technical areas, and site-specific optimization of LID parameters. Research and improvements in these areas will allow better mitigation of climate-change-induced urban floods in a cost-effective manner and will also assist in the achievement of sustainable development goals for Srinagar city and will help us to tackle the increasing problems of water logging and floods in the summer capital of Jammu and Kashmir. Keywords: Climate change, Urban floods, stormwater management, Low Impact Development, Srinagar city, Drainage in Srinagar, Pluvial flooding.

Improvement of simulating sub-daily hydrological impacts of rainwater harvesting for landscape irrigation with rain barrels/cisterns in the SWAT model

Rain barrels/cisterns, a popular type of low impact development (LID) practice, can restore urban hydrological processes and decrease municipal water use by harvesting roof runoff for later use, such as landscape irrigation. However, tools to assist decision makers in creating efficient rainwater harvesting and reuse strategies are limited. This study improved the Soil and Water Assessment Tool (SWAT) in simulating the subdaily hydrological impacts of rainwater harvesting for landscape irrigation with rain barrels/cisterns, including the simulation of rainwater harvesting with rain barrels/cisterns, rainwater reuse for auto landscape irrigation, evapotranspiration, initial abstraction, impervious area, soil profile, and lawn management operation. The improved SWAT was applied in the urbanized Brentwood watershed (Austin, TX) to evaluate its applicability and investigate the impacts of rainwater harvesting and reuse strategies on the reductions and reduction efficiencies (reductions per volume of rain barrels/cisterns implemented) of field scale runoff (peak and depth) and watershed scale streamflow (peak and volume) for two storm events. Scenarios explored included different sizes of rain barrels/cisterns, percentages of rooftop areas with rain barrels/cisterns implemented, auto landscape irrigation rates, and landscape irrigation starting times. The performance of rainwater harvesting and reuse strategies, which is determined by features of fields, watersheds, and storm events, varied for different reduction goals (streamflow or runoff, and peak or depth/volume). For instance, the scenario with rain barrel/cistern sizes of 7.5 mm (design runoff depth from treated roof area) and the scenario with 10% of suitable area implemented with rain barrels/cisterns provided the highest peak streamflow reduction efficiency and total streamflow volume reduction efficiency at the watershed scale, respectively for the smaller storm event. To achieve sustainable urban stormwater management, the improved SWAT model has enhanced capability to help stakeholders create efficient rainwater harvesting and reuse strategies to reduce field scale runoff and watershed scale streamflow.

Evapotranspiration Measurement and Estimation of Crop Coefficient for Native Plant Species of Green Roof in the Tropics

Extensive green roof is one of the sustainable urban stormwater management alternatives to manage and mitigate the urban surface runoff. In order to implement green roofs more effectively, suitable plant species and substrate components for tropical climate must be identified. The aim of this study is to investigate the evapotranspiration (ET) behaviors in extensive green roofs based on different substrate types and local native plant species. Four green roof test beds containing pro-mixing pot and burn soils were each vegetated with Axonopus Compressus (grass) and Portulaca Grandiflora (sedum). A weather station with soil moisture sensors was installed to measure the weather and soil moisture data. The results showed that the mean ET rates for grass-pot soil, sedum-pot soil, grass-burn soil and sedum-burn soil were 1.32 ± 0.41 mm/day, 2.31 ± 0.72 mm/day, 1.47 ± 0.39 mm/day and 2.31 ± 0.43 mm/day, respectively. It is noted that environmental parameters such as ambient temperature, solar radiation and wind speed showed significantly positive relationship (p value < 0.01) with ET rates of green roofs except relative humidity. The crop coefficients (Ks) for the studied green roof plant species are estimated based on actual and reference evapotranspiration rates. The sedum planted in burn soil showed the highest crop coefficient (0.64), followed by sedum in pot soil (0.62), grass in burn soil (0.39) and grass in pot soils (0.37), respectively. The findings in this study also showed that substrate with better water retention capacity generally improved the Ks values.

Probabilistic assessment of hydrologic retention performance of green roof considering aleatory and epistemic uncertainties

Abstract Green roofs (GRs) are well known for source control of runoff quantity in sustainable urban stormwater management. By considering the inherent randomness of rainfall characteristics, this study derives the probability distribution of rainfall retention ratio and its statistical moments. The distribution function of can be used to establish a unique relationship between target retention ratio , achievable reliability AR, and substrate depth h for the aleatory-based probabilistic (AP) GR design. However, uncertainties of epistemic nature also exist in the AP GR model that makes AR uncertain. In the paper, the treatment of epistemic uncertainty in the AP GR model is presented and implemented for the uncertainty quantification of AR. It is shown that design without considering epistemic uncertainties by the AP GR model yields about 50% confidence of meeting . A procedure is presented to determine the design substrate depth having the stipulated confidence to satisfy and target achievable reliability .